Question

The degree of the differential equation
${\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^{5/3}=\frac{d^{2}y}{d{x}^2}$ is

• A. $1$
• B. $5$
• C. $\frac{10}{3}$
• D. $3$

Answer 1

Answer: (D)

The given differential equation is

${\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^{5/3}=\frac{d^{2}y}{d{x}^2}$

$\Rightarrow {\left(\frac{d^{2}y}{dx}\right)}^3={\left[1+{\left(\frac{dy}{dx}\right)}^2\right]}^5$

From above it is clear that the degree of the given differential equation is $3$.